while dividing by node \(i\)  (\(j\) ) degree \(d_{i}\)  (\(d_{j}\) ) is equivalent to
product with the \(ij\) -th element of the \(N\times N\)  matrix \((\tilde{d}\cdot u^{T})_{ij}\)  and \((u\cdot \tilde{d}^{T})_{ij}\) , respectively. By implementing
matrix notations (REF ), (REF ),
(REF ) and (REF ) into the governing equation (REF ) and by applying the distributive property of the Hadamard product [1]} we obtain:
\(\begin{aligned} x[k+1] -x[k] =& \bigg (\left(u\cdot x^{T}[k] - x[k]\cdot u^{T}\right) \circ A\circ \\& \left(u \cdot \tilde{d}^{T}\right) \circ \left(\tilde{d} \cdot u^{T}\right) \circ \Big (\left(\alpha + \delta \right) \cdot \left(A^{2} + A\right) - \\& \frac{1}{2} \delta \cdot \left(u\cdot d^{T} + d\cdot u^{T }\right)\Big )\bigg )\cdot u.\end{aligned}\) 
